Related papers: Simple variational approaches to quantum wells
A short introduction of a relation between a Green's function and a quantum wave impedance function as well as its application to a determination of eigenenergies and eigenfunctions of a quatum-mechanical system is provided. Three different…
The discrete-time, the quantum, and the continuous calculus of variations have been recently unified and extended. Two approaches are followed in the literature: one dealing with minimization of delta integrals; the other dealing with…
This work is mainly based on some theoretical surveys on two dimensional quantum gravitational well, considering harmonic oscillator potential causes an effective plank constant. We find that there is a similarity between two different…
We propose a variational scheme to represent composite quantum systems using multiple parameterized functions of varying accuracies on both classical and quantum hardware. The approach follows the variational principle over the entire…
We study the motion of a classical particle interacting with one, two, and finally an infinite chain of 1D square wells with oscillating depth. For a single well we find complicated scattering behavior even though there is no topological…
The notion of a double well potential typically involves two regions of space separated by a repulsive potential barrier. The solution is a wave function that is suppressed in the barrier region and localized in the two surrounding regions.…
Representative wave functions, which encode the topological properties of the spin polarized fractional quantum Hall states in the lowest Landau level, can be expressed in terms of correlation functions in conformal field theories. Until…
Hamiltonians of a wide-spread class of $G_{inv}$-invariant nonlinear quantum models, including multiboson and frequency conversion ones, are expressed as non-linear functions of $sl(2)$ generators. It enables us to use standard variational…
We present a simple method to deal with caustics in the semiclassical approximation to the partition function of a one-dimensional quantum system. The procedure, which makes use of complex trajectories, is applied to the quartic double-well…
Hybrid quantum/classical variational algorithms can be implemented on noisy intermediate-scale quantum computers and can be used to find solutions for combinatorial optimization problems. Approaches discussed in the literature minimize the…
We investigate the longstanding problem of thermalization of quantum systems coupled to an environment by focusing on a bistable quartic oscillator interacting with a finite number of harmonic oscillators. In order to overcome the…
The eigenvalue equations for the energy of bound states of a particle in a square well are solved, and the exact solutions are obtained, as power series. Accurate analytical approximate solutions are also given. The application of these…
We propose a method for finding gaps in the spectrum of a differential operator. When applied to the one-dimensional Hamiltonian of the quartic oscillator, a simple algebraic algorithm is proposed that, step by step, separates with a…
Any constructive continuous function must have a gradually varied approximation in compact space. However, the refinement of domain for $\sigma-$-net might be very small. Keeping the original discretization (square or triangulation), can we…
We give an explicit formula, as a formal differential operator, for quantum microformal morphisms of (super)manifolds that we introduced earlier. Such quantum microformal morphisms are essentially oscillatory integral operators or Fourier…
We apply the connected moments expansion to simple quantum--mechanical examples and show that under some conditions the main equations of the approach are no longer valid. In particular we consider two--level systems, the harmonic…
In many time-harmonic electromagnetic wave problems, the considered geometry exhibits an axial symmetry. In this case, by exploiting a Fourier expansion along the azimuthal direction, fully three-dimensional (3D) calculations can be carried…
Quantum Hall bilayer systems at filling fractions near \nu = 1/2 + 1/2 undergo a transition from a compressible phase with strong intralayer correlation to an incompressible phase with strong interlayer correlations as the layer separation…
Effective Hamiltonian for the kicked double well system was derived using the Campbell-Baker-Hausdorff expansion formula. Asymmetric model for the kicked system was constructed. Analytical description of the quasienergy levels splittings…
We present a simple way to quantize the well-known Margulis expander map. The result is a quantum expander which acts on discrete Wigner functions in the same way the classical Margulis expander acts on probability distributions. The…